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Hand-y way to remember Unit Circle exact values

Confused, much?

Confused, much?

I was recently working with a Year 10 Mathematical Methods student, in preparation for the upcoming exams. She couldn’t remember the exact values of the Unit Circle angles, so I showed her a handy method of remembering. She was impressed (aw, shucks!), so I thought I’d share it here!

Step 1:

Label the thumb of your left hand “SINE”, your index finger “30”, your middle finger “45”, your ring finger “60” and your pinky “COS”. Draw a vinculum with the number 2 as the denominator on your palm. Or, draw divided by 2 on your palm – whichever works! :)

See below:

Marked Hand


Step 2:

Step 2 requires some imagination. I want you to imagine that there is a magic square root symbol floating in the air above your fingertips. Can you see it?

Magic Root


Step 3:

If you would like to know what the exact value of, say, Sine 30 degrees, fold down the finger with “30” on it. Like this:


The Magic Root symbol goes over the digit left standing on the Sine side of the hand – in this case the thumb. The root of one (or just one), divided by two – the exact value of Sine 30 is one-half!

Can you also see how the Cosine of 30 can be found?

Below I have lowered the “45” digit – the Sine and Cosine of 45 both equal to root two divided by two! It’s magic!




This little memory trick has worked wonders for  me over the past few years, particularly with students who have found surds and fractions to be a frightening mix. I have taught this to students in Year 10, who have found it an invaluable tool in their understanding of the Unit Circle.


Here’s a challenge for you or your students. How can we include the exact values for the Tangent into this? :)


Twitter and Blogging..

Ok, it’s official, my head just exploded. Following an #edchat on Twitter will do that to you!




One of the great things about having a broad and dynamic Professional Learning Network is that, just when you feel like it’s all a bit too hard, something comes along and stokes the fires again.

Tonight I was participating in the #aussieED Twitter EdChat about the benefits of blogging both for students and for teachers. Some great individuals (@MRsalakas, @ZeinaChalich, just to name a few!) have shared their thoughts on what makes a good blog and how educators can use blogging to amplify the voices of ourselves and our students.

What I also found inspiring was the simple suggestions of everyday teachers from around the world on how we can better leverage blogging as a learning opportunity.


#1, Get started (that’s my tip!)

#2. Write for you, not for others (@GeoMouldey)

#3 Keep it short (@diPrato)

#4 Focus on the ‘do’s’ rather than the ‘don’ts’ (@mythsysizer)

#5 Don’t get discouraged! (@joprestia)